Nanoparticle optical tweezers based on quasi-continuum bound state

Abstract

The invention relates to nano particle optical tweezers based on a quasi-continuum bound state, and belongs to the technical field of optical tweezers. According to the invention, a quasi-continuum bound state mode is excited on the asymmetric photonic crystal flat plate, and the structure realizes high-performance nanoparticle capture. Specifically, the photonic crystal flat plate is realized by introducing a periodic asymmetric nanopore array on a silicon plate. The lower side of the flat plate is a silicon oxide substrate, the upper side is water, and nanoparticles in the aqueous solution can be captured by optical tweezers. When the material of the nanoparticles captured by the optical tweezers is silicon and the diameter is 60nm, the capturing force and the capturing potential are respectively-93.29 pN / mW and 1706.17 kBT. Compared with other photonic crystal nanoparticle optical tweezers, the capturing performance is remarkably improved, and a high-stability capturing trap can be obtained under low input optical power.

Description

Technical Field

[0001] The invention relates to a nanoparticle optical tweezers based on a quasi-continuum bound state, which is characterized by high capture force and high potential well depth and can realize near-field capture of nanoparticles, belonging to the technical field of optical tweezers. Background Art

[0002] Optical tweezers are widely used in biomedicine, materials science, chemical industry and space exploration (Document 1: YiZhang, Jingyi Zhao, Zhiyuan Che and Lei Shi. "Optical trapping using quasi-boundstates in the continuum of photonic crystal slab." Optics Express 32.22 (2024): 39906-39914; Document 2: Lichao Zheng, Esha Maqbool and Zhanghua Han. "Efficient and Shape-Sensitive Manipulation of Nanoparticles by Quasi-Bound States in the Continuum Modes in Al1-Dielectric Metasurfaces." Micromachines 15.4 (2024): 437.). Since continuum bound states have strong light field localization characteristics and large mode volume, combining them with optical tweezers can effectively improve the particle capture performance of optical tweezers (Reference 3: Haoye Qin, Yuzhi Shi, Zengping Su, Guodan Wei, Zhanshan Wang, Xinbin Cheng, Ai Qun Liu, Patrice Genevet and Qinghua Song. "Exploiting extraordinary topological optical forces at bound states in the continuum." Science Advances 8.49 (2022): eade7556.). Continuum bound states can be used as a method to manipulate light and enhance the interaction between light and matter on a subwavelength scale, but in practical applications, due to limited structural range, material absorption and other external disturbances, quasi-continuum bound states with limited quality factors will appear.By introducing appropriate perturbations, the continuum bound state can be converted into a quasi-continuum bound state mode with high quality factor and high field enhancement, so that it can be combined with optical tweezers for particle trapping (Reference 4: Shaimaa I. Azzam and Alexander V. Kildishev. "Photonic bound states in the continuum: from basics to applications." Advanced Optical Materials 9.1 (2021): 2001469; Reference 5: Md Rabiul Hasan and Olav Gaute). "Metasurface supporting quasi-BIC for optical trapping and Raman-spectroscopy of biological nanoparticles." Optics Express 31.4 (2023): 6782-6795.). Near-field capture of nanoparticles requires field enhancement concentrated in the electric field distribution of low refractive index regions. The quasi-continuum bound state mode with field enhancement concentrated in the low refractive index region is suitable for particle capture. It is challenging to achieve stable particle capture under low-power conditions by regulating the geometric parameters of the structure to excite the electric field distribution that meets the particle capture requirements.

[0003] In order to improve the capture performance of nanoparticle optical tweezers, we weakly destroyed the structural symmetry of the two-dimensional silicon photonic crystal slab. Under the condition of vertical incidence of a plane wave light source, the quasi-continuum bound state mode was excited, which had a strong field enhancement effect and achieved stable capture of nanoparticles under low-power conditions. Summary of the invention

[0004] The present invention slightly destroys the symmetry of the photonic crystal slab and excites a continuum bound state mode, the field enhancement of the electric field distribution corresponding to this mode is concentrated in the low refractive index region, this mode is suitable for particle capture, and a nanoparticle optical tweezers based on the quasi-continuum bound state is proposed.

[0005] 1. Specific content of the present invention

[0006] (1) The present invention designs a photonic crystal slab structure that can support quasi-continuum bound state resonant modes, such as Figure 1 As shown, a single unit cell of the photonic crystal slab includes a circular hole and a penetrating square groove, and the center of the square groove does not coincide with the center of the unit cell.

[0007] (2) The designed structure excites a quasi-continuum bound state mode at 1539.39 nm when a plane wave light source is incident vertically, such as Figure 2 shown.

[0008] (3) The asymmetry of the structure is reflected in the distances between the upper and lower boundaries of the square groove and the center of the unit cell, which are a1 = 50 nm and a2 = 30 nm, respectively. The other structural parameters were determined after optimization as follows: lattice constant P = 780 nm, thickness of the photonic crystal plate h1 = 100 nm, thickness of the silica substrate h2 = 3950 nm, diameter of the circular hole d = 200 nm, and width of the square groove a = 80 nm.

[0009] 2. The advantages of the present invention are as follows:

[0010] (1) Compared with symmetrically structured nanoparticle optical tweezers, the present invention effectively increases the optical force exerted on the nanoparticles and reduces the input power required to achieve stable capture.

[0011] (2) The capture force of the nanoparticles involved in the present invention can be significantly enhanced by adjusting the asymmetric parameters of the structure.

[0012] (3) The light field of the capture mode of the present invention is localized in the low refractive index region and has a strong field enhancement effect. This strongly enhanced light field can effectively capture nanoparticles.

[0013] 3. The principles of the present invention are as follows:

[0014] (1) Quasi-continuum bound states can be excited by breaking the symmetry of the structure. The light field of the quasi-continuum bound state can be coupled with free space while maintaining a strong field enhancement effect.

[0015] (2) Quasi-continuum bound state modes can form strong local field enhancement at specific locations. This enhanced light field can generate strong optical gradient forces.

[0016] (3) When the nanoparticle approaches the structure, it is attracted to the field enhancement region by the optical gradient force and is stably confined at this location due to the sufficiently large potential well depth generated by the optical force. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 (a) is a three-dimensional schematic diagram of the designed photonic crystal slab. The photonic crystal slab is obtained by etching a periodic array on a silicon plate. The photonic crystal slab is placed on a silicon dioxide (SiO2) substrate. Figure 1 (b) and Figure 1(c) are the top view and side view of the unit cell. The structural parameters are: lattice constant P = 780nm, photonic crystal plate thickness h1 = 100nm, silicon dioxide substrate thickness h2 = 3950nm, circular hole diameter d = 200nm, square groove width a = 80nm, and the distances from the upper and lower boundaries of the square groove to the center of the unit cell are a1 = 50nm and a2 = 30nm respectively.

[0018] Figure 2 The transmission spectra of the symmetric structure (top) and the asymmetric structure (bottom) are compared. The asymmetric structure supports the quasi-continuum bound state mode, and the resonant wavelength is 1539.39nm.

[0019] Figure 3 (a) is the electric field distribution diagram of the resonance mode with a resonance wavelength of 1539.39 nm in the xy plane (z=0). Figure 3 (b) Electric field distribution diagram of the 1539.39 nm resonance mode in the xZ plane (y=0).

[0020] Figure 4 The optical force map is obtained by simulating a silicon particle with a diameter of 60nm near the structure. Figure 4 (a) is the optical force diagram of the particle simulated using the MST method from 0 to 340 nm along the x direction (y = 10 nm, z = 0). The maximum optical force on the particle along this path in the x direction reaches 78.47 pN / mW. Figure 4 (b) is the optical force diagram simulated using the MST method on the particle along the z direction (x=175nm, y=10nm), from -10nm to 220nm. The maximum optical force on the particle along this path in the z direction reaches -93.29pN / mW (the negative sign represents that the direction of the force on the particle is along the negative direction of the z axis).

[0021] Figure 5 This is the potential well distribution diagram of a silicon particle with a diameter of 60nm near the structure. Figure 5 (a) is the optical potential well diagram of the particle along the x direction. The potential well depth along the x direction reaches 1667.48k B T; Figure 5 (b) is the optical potential well diagram of the particle along the z direction. The potential well depth along the z direction reaches 1706.17k B T.

[0022] Figure 6 It is the optical force in the z direction of a silicon particle with a diameter of 60nm at a specific position (x=175nm, y=10nm, z=60nm) when the structural parameters (a1-a2) change (a remains unchanged). The optical force shows a clear increasing trend as the structural parameters decrease. DETAILED DESCRIPTION

[0023] In order to make the objectives, technical solutions and advantages of the present invention more clear, the specific structure, principle and sensing characteristics of the present invention are further described below in conjunction with the accompanying drawings.

[0024] The present invention proposes to break the symmetry of the two-dimensional photonic crystal plate to stimulate the quasi-continuum bound state mode. The light field of the quasi-continuum bound state can be coupled with the free space while maintaining a strong field enhancement effect. This mode can form a strong local field enhancement at a specific position. This enhanced light field can generate a strong optical gradient force. The three-dimensional structure schematic diagram of the designed asymmetric photonic crystal plate is shown in Figure 2. Figure 1 As shown in (a), a photonic crystal slab is formed by etching a periodic array of nanoholes on a silicon plate. The structural parameters of a single unit cell are shown in Figure 1 (b) and Figure 1 As shown in (c), the structural parameters are: lattice constant P = 780nm, photonic crystal plate thickness h1 = 100nm, silicon dioxide substrate thickness h2 = 3950nm, circular hole diameter d = 200nm, square groove width a = 80nm, and the distances between the upper and lower boundaries of the square groove and the center of the unit cell are a1 = 50nm and a2 = 30nm respectively.

[0025] Since the upper and lower boundaries of the square groove in a single unit cell are at different distances from the center of the unit cell, the asymmetry of the structure creates conditions for the excitation of quasi-continuum bound states. Figure 2 The transmission spectra of the symmetric structure (top) and the asymmetric structure (bottom) are shown. The simulation results show that when the symmetry of the structure is broken, a quasi-continuum bound state mode appears at 1539.39nm.

[0026] The electric field in the capture mode is analyzed below. Figure 3 (a) and (b) show the electric field distribution of the resonant mode with a resonant wavelength of 1539.39 nm in the xy plane (z = 0) and xz plane (y = 0). The electric field of the quasi-continuum bound state mode is mainly distributed in the square slot area on both sides of the circular hole, which means that particle capture can be performed near the square slot area on both sides of the circular hole.

[0027] Regarding the analytical calculation of the optical force acting on the particles, the particles will be affected by the combined effects of the optical gradient force and the scattering force in the light field. However, due to the high electric field enhancement near the square slot area, the scattering force can be ignored. The Maxwell stress tensor (MST) method is used to calculate the optical gradient force.

[0028] F=∮ s ( <T M >·n)dS (1)

[0029] in <T M > represents the Maxwell stress tensor, and n is the normal vector of the outer surface S. <TM > can be expressed as

[0030]

[0031] Where D is the electric displacement, H is the magnetic field strength, E * and B * are the complex conjugates of the electric field intensity and the magnetic induction intensity respectively, and I is the isotropy tensor.

[0032] A spherical silicon particle with a diameter of 60 nm is placed near the square groove area. By changing the position of the particle in the x direction along the path (y = 10 nm, z = 0), the distribution of the component of the optical force on the particle in the x direction is calculated and analyzed according to equations (1) and (2). The results are shown in the figure. Figure 4 (a) shows that when the particle is at x = 100nm, the optical force in the x direction is the largest, reaching 78.47pN / mW. The direction of the optical force is pointing to the position of x = 175nm. Therefore, under the action of the x-direction component of the optical force, the particle will stabilize at approximately the position of x = 175nm on this path.

[0033] By changing the position of the particle in the z direction along the path (x = 175nm, y = 10nm), the distribution of the component of the optical force on the particle in the z direction is calculated and analyzed according to equations (1) and (2). The results are as follows: Figure 4 (b) shows that when the particle is at z = 60nm, the optical force in the z direction is the largest, reaching -93.29pN / mW (the negative sign represents that the direction of the force on the particle is along the negative direction of the z axis). The direction of the optical force points to z = 0. Therefore, under the action of the optical force in the z direction, the particle will stabilize at the z = 0 position on this path. Figure 6 The relationship between the capture force of the particle at a specific position (x=175nm, y=10nm, z=60nm) and the structural parameter (a1-a2) is shown. When the structural parameter decreases, the capture force of the particle is significantly enhanced.

[0034] The potential well depth can be calculated by integrating the components of the optical force along a particular path, as:

[0035] U x =-∫F x dx (3)

[0036] According to formula (3), the horizontal component of the optical force F x Integrating from 0 to 340 nm on the x-axis, the potential well depth curve is as follows: Figure 5 (a) As shown in the figure, the maximum potential well depth is obtained at about x = 175nm, U xmax =1667.48k B T. According to formula (3), the vertical component of the optical force F ZIntegrating from -10nm to 220nm on the z-axis, the potential well depth curve is as follows Figure 5 (b) As shown in the figure, the maximum potential well depth is obtained at z = 0, U z max =1706.17k B T. Therefore, this position (x=175nm, z=0) is the optical trap position where the particle is finally trapped, which is consistent with the capture mode obtained by photomechanical analysis, and the maximum potential well depth ensures the stability of the trapping.

Claims

1. A nanoparticle optical tweezer based on a quasi-continuum bound state is proposed, characterized in that: a photonic crystal slab is formed by etching a periodic asymmetric array of central circular holes on a silicon plate, the photonic crystal slab is placed on a silicon dioxide (SiO2) substrate, the environment on the upper side and the area inside the hole is water, and the thickness of the photonic crystal slab is 100nm.

2. The periodic array according to claim 1, characterized in that: The radius of the central circular hole of each unit cell is 100 nm, the size of the square groove is 80 nm × 780 nm, the upward offset is 10 nm, and the lattice constant of the periodic array is 780 nm.

3. The nanoparticle optical tweezers structure design based on quasi-continuum bound state according to claim 1, characterized in that: The slight destruction of the structural symmetry creates conditions for the excitation of the quasi-continuum bound state, and the resonance wavelength of the mode is 1539.39nm. By exciting the resonant mode, field enhancement is obtained to capture the nanoparticles.

4. According to the contents of claims 1, 2 and 3, it is characterized in that: By adjusting the structural parameters, the capture force of the nanoparticles was significantly enhanced. The optical force on the silicon particle with a radius of 60nm was -93.29pN / mW, and the potential well depth was 1706.17k. B T.

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